Answer:
Option A. [tex]AB=25\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
If AB is a mid-segment, then AB is parallel to YZ
so
Triangles AXB and YXZ are similar by AA Similarity Theorem
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
[tex]\frac{YZ}{AB}=\frac{YX}{AX}[/tex]
we have that
[tex]AB=\frac{1}{2}YZ[/tex] ----> by Midpoint Theorem
[tex]YZ=2AB[/tex]
substitute the given values in the expression above
[tex]\frac{2AB}{AB}=\frac{22+2x+2}{2x+2}[/tex]
solve for x
[tex]2=\frac{24+2x}{2x+2}[/tex]
Multiply by (2x+2) both sides
[tex]4x+4=2x+24[/tex]
Group terms
[tex]4x-2x=24-4[/tex]
[tex]2x=20[/tex]
[tex]x=10[/tex]
step 2
Find the length of AB
[tex]AB=3x-5[/tex]
substitute the value of x
[tex]AB=3(10)-5=25\ units[/tex]
